B = `x^{5} – 2021x^{4} + 2021x^{3} – 2021x^{2} + 2021x – 1000` tại `x = 2020`

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1. Đáp án:

   `text{Đề : Tính B (x)}` `= x^5 – 2021 x^4 + 2021 x^3 – 2021x^2 + 2021x – 1000`

   `text{Ta có : B (2020)}`

   `-> x = 2020`

   `-> x + 1 = 2021 (1)`

   `text{Ta có : B (x)}` `= x^5 – 2021 x^4 + 2021 x^3 – 2021x^2 + 2021x – 1000`

   `text{Thay (1) vào ta được :}`

   `⇔ B (x) = x^5 – (x + 1) x^4 + (x + 1) x^3 – (x + 1) x^2 + (x + 1)x – 1000`

   `⇔ B (x) = x^5 – x^5 – x^4 + x^4 + x^3 – x^3 – x^2 + x^2 + x – 1000`

   `⇔ B (x) = (x^5 – x^5) + (-x^4 + x^4) + (x^3 – x^3) + (-x^2 + x^2) + (x – 1000)`

   `⇔ B (x) = x -1000`

   `⇔ B (2020) = 2020 – 1000`

   `⇔ B (2020) = 1020`

   `text{Vậy B  (2020) = 1020}`

    

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2. B = $x^{5}$ – 2021$x^{4}$ + 2021$x^{3}$ – 2021$x^{2}$ + 2021x – 1000

   ⇒  B = $x^{5}$ – 2020$x^{4}$ – $x^{4}$ + 2020$x^{3}$ + $x^{3}$ – 2020$x^{2}$ – $x^{2}$ + 2020x + x – 2020 + 1020

   ⇒ B = $x^{4}$ (x – 2020) – $x^{3}$ (x – 2020) + $x^{2}$ (x – 2020) – x(x – 2020) + (x – 2020) + 1020

   Ta có: x = 2020 ⇒ x – 2020 = 0

   ⇒ B = $2020^{4}$ . 0 – $2020^{3}$. 0 + $2020^{2}$. 0 – 2020 . 0 + 0 + 1020

   ⇒ B = 0 – 0 + 0 – 0 + 0 + 1020

   ⇒ B = 1020

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